[10000ダウンロード済み√] y=a(1+r)^t examples 215580-Y=a(1+r)^t examples

Measurable Success can be measured by the number of applications, interviews and job offersSection 16 Vector Functions We first saw vector functions back when we were looking at the Equation of LinesIn that section we talked about them because we wrote down the equation of a line in \({\mathbb{R}^3}\) in terms of a vector function (sometimes called a vectorvalued function)In this section we want to look a little closer at them and we also want to look at some vector functionsDefinition In the case of a space curve, the radius of curvature is the length of the curvature vector In the case of a plane curve, then R is the absolute value of ≡ =, where s is the arc length from a fixed point on the curve, φ is the tangential angle and κ is the curvature Formula In 2D If the curve is given in Cartesian coordinates as y(x), then the radius of curvature is

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Y=a(1+r)^t examples

Y=a(1+r)^t examples-The characteristic equation is r2 5 r 4 = (r 1)(r 4) = 0, the roots of the polynomial are r = −1 and −4 The general solution is then y = C1 e −t C 2 e −4t Suppose there are initial conditions y(0) = 1, y′(0) = −7 A unique particular solution can be found by solving for C1 and C2 using the initial conditions First weIn this section we solve linear first order differential equations, ie differential equations in the form y' p(t) y = g(t) We give an in depth overview of the process used to solve this type of differential equation as well as a derivation of the formula needed for the integrating factor used in the solution process

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Y Write the exponential growth function= a(1 r)t = 150,000(1 008)t Substitute 150,000 for a and 008 for r Add= 150,000(108)t The festival attendance can be represented by y = 150,000(108)t b The value t = 4 represents the fi fth year because t = 0 represents the fi rst year y = 150,000(108)t Write the exponential growth function# A formula y ~ x # A converted formula y = a_1 a_2 * x This is an example of a simple conversion y ~ x gets translated into y = a_1 a_2 * x To see and understand what R actually happens, you can use the model_matrix() function This function creates a design or model matrix by, for example, expanding factors to a set of dummy variables, depending on the contrasts, and expanding interactions similarlySpeed, r = 48 miles/hour Step 2

At any point along the path, the (small) tangent vector ${\bf r}'\,\Delta t$ gives an approximation to its motion over a short time $\Delta t$, so the work done during that time is approximately ${\bf F}\cdot{\bf r}'\,\Delta t$;= 1 r Subtracting 1, you get that the rate is just over 003 or 3/10 of 1% The function that would model your growth is y = 484(1003)^t To do #2, find out how many years each year is after 1980, and plug those numbers in for "t" For example, to find 1985, you'd take 484(1003)^5 To do #3, "double" the original population would be 968 million peopleFor t and r must be the same Example of Exponential Growth The 00 census found that a US Population of about 281 million with an estimated growth rate of 07% Q = Q0 x (1 r)t 4/1/10 2 Forms of the Exponential

1 Loop Examples 11 Example Sum Primes Let's say we wanted to sum all 1, 2, and 3 digit prime numbers To accomplish this, we could loop through all 1, 2, and 3 digit integers, testing if each is a prime number (using the isprime function) If and only if a particular value is prime, then we'll add it to our running totalUsing the growth formula we have y = a(1 r) x where a = 1 (we start with 1 bacteria), and r = 100%, since the amount doubles y = 1(1 100) x = 2 x (same result) Notice that the graph is a scatter plot You cannot have a fractional part of a bacteria The dotted line is the exponential function which contains the scatter plots (the model)Example x 0 = 50 r = 4% = 004 t = 90 hours x(t) = x 0 × (1 r) t = 50×(1004) 90 = 1706 Exponent calculator

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Example Example 321 Let R be the relation on the set R real numbers defined by xRy iff x−y is an integer Prove that R is an equivalence relation on R Proof I Reflexive Suppose x ∈ R Then x−x = 0, which is an integer Thus, xRx II Symmetric Suppose x,y ∈ R and xRy Then x − y is an integerEXAMPLE 1 (a) Find the derivative of r(t) = (2 t3)i te−tj sin(6t)k (b) Find the unit tangent vector at the point t = 0 SOLUTION (a) According to this theorem, we differentiate each component of r r'(t) = Correct Your answer is correctMeasurable Success can be measured by the number of applications, interviews and job offers

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Warm­up y = a(1r)t 10) 00(1 003)1 = $60 11) 0(1 003)10 = $ 12) 600(1 007)4 =$ 13) 1500(1 004)8 = $5285There is a substantial number of processes for which you can use this exponential growth calculator The general rule of thumb is that the exponential growth formula x(t) = x 0 * (1 r/100) t is used when there is a quantity with an initial value, x 0, that changes over time, t, with a constant rate of change, rThe exponential function appearing in the above formula has a base equal to 1P = C (1 r) t Continuous Compound Interest When interest is compounded continually (ie n > ), the compound interest equation takes the form P = C e rt Demonstration of Various Compounding The following table shows the final principal (P), after t = 1 year, of an account initially with C = $, at 6% interest rate, with the given

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Suppose that the path of an object is given by a vector function ${\bf r}(t)$;61 INTRO TO LINEAR TRANSFORMATION 191 1 Let V,W be two vector spaces Define T V → W as T(v) = 0 for all v ∈ V Then T is a linear transformation, to be called the zero transOneSample ttest The onesample ttest, also known as the singleparameter t test or singlesample ttest, is used to compare the mean of one sample to a known standard (or theoretical / hypothetical) mean Generally, the theoretical mean comes from a previous experiment For example, comparing whether the mean weight of mice differs from 0 mg, a value determined in a previous study

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This equation gives the amount B that the person still needs to repay after t years B = A (1 r/n) NT P (1 r/n) NT 1 (1 r/n) 1 where B = balance after t years A = amount borrowed n = number of payments per year P = amount paid per paymentAnd = 2 2 2 2!Example 12 Find the length of ~r(t) =~it2~j t3~k for 0 6 t 6 1 This is straight forward calculations L = Z 1 0

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